fix(mentor): restore Add Project on mentoring rounds + gate mentor assignment

Three related bugs around the mentoring-round Projects tab:

1. Add Project to Round was unreachable on MENTORING rounds — the table swap
   in the prior commit lost the button. Export AddProjectDialog from
   project-states-table and render it inside MentoringProjectsTable with an
   "Add" button in the filter row and a CTA in the empty state.
2. The "Assign Projects" quick action on the round overview linked to the
   global pool with an opaque filter; on MENTORING rounds it now switches
   to the Projects tab where the new Add Project button + auto-fill +
   per-team picker all live. Non-mentoring rounds keep the old behavior.
3. mentor.assign and mentor.bulkAssign now refuse projects that aren't
   enrolled in any MENTORING round (any status). The single-assign throws
   BAD_REQUEST with a guidance message; the bulk path filters them out and
   reports ineligibleProjectCount in the result so the UI can warn the
   admin instead of silently skipping.

Tests: the multi-mentor-assignment suite now sets up a MENTORING round +
ProjectRoundState for each project it tests against, matching the new gate.

src/server/routers/mentor.ts

@@ -370,6 +370,25 @@ export const mentorRouter = router({
         where: { id: input.projectId },
       })
 
+      // Gate: the project MUST be in a MENTORING round (any status, including
+      // DRAFT, ACTIVE, or CLOSED). We do not allow mentor assignment for
+      // projects that aren't part of a mentoring round — those should be
+      // added to a mentoring round first.
+      const inMentoringRound = await ctx.prisma.projectRoundState.findFirst({
+        where: {
+          projectId: input.projectId,
+          round: { roundType: 'MENTORING' },
+        },
+        select: { id: true },
+      })
+      if (!inMentoringRound) {
+        throw new TRPCError({
+          code: 'BAD_REQUEST',
+          message:
+            'This project is not in a mentoring round. Add it to a mentoring round first, then assign mentors.',
+        })
+      }
+
       // Verify mentor exists
       const mentor = await ctx.prisma.user.findUniqueOrThrow({
         where: { id: input.mentorId },
@@ -704,7 +723,13 @@ export const mentorRouter = router({
       }
 
       const projects = await ctx.prisma.project.findMany({
-        where: { id: { in: input.projectIds } },
+        where: {
+          id: { in: input.projectIds },
+          // Gate: only projects that are in some MENTORING round (any status)
+          projectRoundStates: {
+            some: { round: { roundType: 'MENTORING' } },
+          },
+        },
         select: {
           id: true,
           title: true,
@@ -718,6 +743,16 @@ export const mentorRouter = router({
         },
       })
 
+      if (projects.length === 0) {
+        throw new TRPCError({
+          code: 'BAD_REQUEST',
+          message:
+            'None of the selected projects are in a mentoring round. Add them to a mentoring round first.',
+        })
+      }
+
+      const ineligibleCount = input.projectIds.length - projects.length
+
       // Track per-mentor (for emails) and per-project (for team intros) state.
       const perMentor = new Map<
         string,
@@ -884,6 +919,7 @@ export const mentorRouter = router({
       return {
         totalAssigned,
         totalSkipped,
+        ineligibleProjectCount: ineligibleCount,
         touchedProjectCount: touchedProjectIds.size,
         perMentor: Array.from(perMentor.entries()).map(([id, b]) => ({
           mentorId: id,